This is a series of invited colloquiual lectures provided by top researchers in the field of systems biology, theoretical and computational biology, bioinformatics and related fields of applied mathematics and computer science. The series is prepared in collaboration with Global Change Research Centre AS CR as a part of the ESF co-funded project CyanoTeam. The project is associated with an international network CyanoNetwork.

Lectures run irregularly during the academic year with respect to the time schedule provided on this web page. Each of the lectures will be announced at least one week in advance.

We consider the problem of synthesizing safe and robust values of timing parameters of cardiac pacemaker models so that a quantitative objective, such as the pacemaker energy consumption or its cardiac output (a heamodynamic indicator of the human heart), is optimised in a finite path. Indeed, safety is of paramount importance in the design of medical devices, and patient's physiological properties has to be maintained in a robust way with respect to parameter perturbations.

In the first part of the lecture, we introduce the formal modelling framework and the synthesis algorithms. We consider models given as parametric networks of timed I/O automata with data, which extend timed I/O automata with priorities, real variables and real-valued functions, and specifications as Counting Metric Temporal Logic (CMTL) formulas. We formulate the parameter synthesis as a bilevel optimisation problem, where the quantitative objective (the outer problem) is optimised in the solution space obtained from optimising an inner problem that yields the maximal robustness for any parameter of the model. We develop an SMT-based method for solving the inner problem exactly through a discrete encoding, and combine it with evolutionary algorithms and simulations to solve the outer optimization task.

In the second part, we discuss the application of this method to the synthesis of pacemaker parameters. We provide a new multi-component heart model, which can reproduce patient-specific heart rhythm and a range of heart diseases, and consider a parametric dual chamber pacemaker model. We apply our approach to find the values of multiple timing parameters of the pacemaker for different heart diseases. Finally, we show how our synthesis method can be used to derive personalised heart models from time-series data.